We have observed the spatial distribution of coherent or resonance transition radiation (RTR) in the soft-x-ray region of the spectrum (1 -3 keV). Resonance transition radiators were constructed and tested at two accelerators using electron-beam energies ranging from 50 to 228 MeV. These radiators emitted soft x rays in a circularly symmetrical annulus with a half-angle divergence of 2.5-9.0 mrad. The angle of peak emission was found to increase with electron-beam energy, in contrast to the incoherent case, for which the angle of emission varied inversely with electron-beam energy. By careful selection of foil thickness and spacing, one may design radiators whose angle of emission varies over a range of chargedparticle energies. A particular RTR mode (r =m =1) was found to give a sharp annular ring that becomes more accentuated as the number of foils is increased. The RTR effect has application in particle detection, beam diagnostics, x-ray source brightness enhancement, and x-ray free-electron-laser emission.